Example: Write the possible resonance
8.9 Formal Charges
• Formal charge (FC) – a charge assigned to atoms
in Lewis structures assuming that the shared e- are
divided equally between the bonded atoms.
– # of e- assigned to an atom in a Lewis structure – all
lone pair e- (L) and half of the shared e- (S)
– # of valence e- of an atom (V)
– # of bonds for an atom (B) → B = S/2
FC = V - [L + S/2] = V - [L + B]
• The FC shows the extent to which atoms have
gained or lost e- in covalent bond formation
• The sum of all FCs equals the charge of the species
• Lewis structures with lower FCs are more stable
Example: Evaluate the stability of the three
NCO-
possible atomic arrangements of the
ion
assuming structures with two double bonds.
a) [:N=C=O:]- b) [:C=N=O:]- c) [:C=O=N:]V
L+B
L+B
L+B
→ 5(N)
→ a) 6(N)
→ b) 4(N)
→ c) 6(N)
4(C)
4(C)
6(C)
6(C)
6(O)
6(O)
6(O)
4(O)
FC → a) -1(N) 0(C) 0(O)
FC → b) +1(N) -2(C) 0(O)
FC → c) -1(N) -2(C) +2(O)
Structure (a) has the lowest formal charges ⇒ most stable
• Biradicals – molecules
with two unpaired electrons
• The Lewis structures of
some biradicals do not show
unpaired electrons (:O=O:)
Example: Write the Lewis structure of NO2.
[O–N–O]
ntot = 5 + 2×
× 6 = 17
nneed = 4 + 2×
× 6 = 16
nrem = 17 - 4 = 13
⇒ add 1 more bond
:O=N–O·
structures of the NCO- ion (N-C-O) including
the formal charges of all atoms.
[N–C–O]ntot = 5 + 4 + 6 + 1 = 16
nrem = 16 - 4 = 12
nneed = 6 + 4 + 6 = 16
nneed > nrem
deficiency of 4 e- ⇒ add 2 more bonds
a) [:N=C=O:]- b) [:N≡
≡ C–O:]- c) [:N–C≡
≡ O:]V
L+B
L+B
L+B
→ 5(N)
→ a) 6(N)
→ b) 5(N)
→ c) 7(N)
4(C)
4(C)
4(C)
4(C)
6(O)
6(O)
7(O)
5(O)
FC → a) -1(N) 0(C) 0(O)
FC → b) 0(N) 0(C) -1(O)
FC → c) -2(N) 0(C) +1(O)
Exceptions to the Octet Rule
8.10 Radicals and Biradicals
• Radicals – odd electron species (·CH3, ·OH,
·NO, ·NO2, …)
– highly reactive and short lived species
– significance to atmospheric chemistry (smog) and
human health (antioxidants)
Example: Write the Lewis structure of NO.
[N–O]
ntot = 5 + 6 = 11
nrem = 11 - 2 = 9
nneed = 6 + 6 = 12
⇒ add 1 more bond
·N=O: ↔ :N=O·
8.11 Expanded Valence Shells
• Extended octets – more than eight electrons
around a central atom
• Extended octets are formed only by atoms with
empty d-orbitals in the valence shell (pelements from the third or later periods)
• Extended octets form when:
– there are too many e- (nneed < nrem) or more than 4
atoms are bonded to the central atom – electronrich structures → place the extra electrons at the
central atom
– structures with lower formal charges can be
achieved by forming an extended octet
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Example: Write the Lewis structure of XeF4.
ntot = 8(Xe) + 4×
× 7(F) = 36
nrem = 36 - 8 = 28
nneed = 0(Xe) + 4×
× 6(F) = 24
nneed < nrem
4 extra e- ⇒ add 2 lone pairs at Xe
Example: Write the Lewis structure of I3-.
ntot = 3×
× 7(I) + 1(charge) = 22
nrem = 22 - 4 = 18
nneed < nrem
nneed = 4(I) + 2×
× 6(I) = 16
2 extra e- ⇒ add 1 extra lone pair at the central I atom
after completing the octets for all atoms
Example: Select the favored resonance
structure of the PO43- anion.
Formal charges:
(a) O → 6-(6+1)=-1
(b) O– → 6-(6+1)=-1
O= → 6-(4+2)=0
P → 5-(0+4)=+1
P → 5-(0+5)=0
• Structure (b) has an extended octet (10 e-) at
the P atom
• Structure (b) is more favored (contributes
more to the resonance hybrid) due to the lower
formal charges
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